I'll assume you are answering "Yes" to all my questions.
If the thermometer instructions prohibit using it for broiling meat, then I suggest you get a digital instant read thermometer you can use to check the temp.
I thought about that and I get concered about opening and closing and checking the meat so many times. - That it will result in uneven cooking, or other continuity issues.
Oh, and also sticking it - makes the juices come out!
I leave the door popped to the first position for broiling. The theory goes that you broil with direct heat. If the door is closed, you are baking. Either way an external read thermometer can be used.